Answer
$135^\circ, 225^\circ$
Work Step by Step
Given $sec\theta=\frac{1}{cos\theta}=-\sqrt 2$ and $\theta\in[0^\circ,360^\circ)$, we have $cos\theta=-\frac{\sqrt 2}{2}$, and we can find $\theta=135^\circ, 225^\circ$
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